Step-by-step explanation:
The given expression is:
25[tex]x^4[/tex] - 64
To find, the equivalent expressions are:
a) 25[tex]x^4[/tex] + 40x - 40x - 64
= 25[tex]x^4[/tex] - 64, is the equivalent expression.
b) 25[tex]x^4[/tex] + 13x - 13x - 64
= 25[tex]x^4[/tex] - 64, is the equivalent expression.
c) (5[tex]x^2[/tex] + 8)(5[tex]x^2[/tex] - 8)
Using the algebraic identity,
(a + b)(a - b) = [tex]a^{2}-b^{2}[/tex]
= [tex](5x^2)^2-8^2[/tex]
= 25[tex]x^4[/tex] - 64, is the equivalent expression.
d) ([tex]x^2[/tex] + 13)([tex]x^2[/tex] - 13)
Using the algebraic identity,
(a + b)(a - b) = [tex]a^{2}-b^{2}[/tex]
= [tex](x^2)^2-13^2[/tex]
= [tex]x^4[/tex] - 169, is not a equivalent expression.
e) [tex](5x^2-8)^2[/tex]
Using the algebraic identity,
[tex](a-b)^{2} =a^{2} -2ab+b^2[/tex]
[tex]= (5x^2)^{2} -2(5x^2)(8)+8^2[/tex]
[tex]= 25x^4 -80x^2+64[/tex], is not a equivalent expression.
∴ The equivalent expression of 25[tex]x^4[/tex] - 64 are "a), b) and c)".
